Physical Review · 1950 · 1.2K citations · 10 references
Materials ScienceOrder TheoryHigh Temperature MaterialsShort-range Order ParametersPhysicsApproximate TheoryEngineeringCondensed Matter PhysicsApplied PhysicsMetallurgical InteractionAlloy DesignSolid MechanicsEnergy TermsThermodynamicsExperimental ObservationsAlloy PhaseMetallurgical SystemMicrostructure
Short‑range order parameters αᵢ describe how an atom in an alloy interacts with atoms in its ith surrounding shell. The study extends the theory to compute configurational energy, specific heat, and order parameters for alloys of arbitrary composition, exemplified by copper‑gold systems. Using approximate thermodynamic reasoning, the authors derive equations linking αᵢ to energy terms and temperature, obtain the long‑range order parameter S in the large‑i limit, and extend the framework to calculate configurational energy, specific heat, and order parameters for arbitrary‑composition alloys. The calculated long‑ and short‑range order parameters agree well with recent x‑ray diffraction data, and the extended theory yields qualitative agreement with experimental observations for alloys such as copper‑gold.
Short-range order parameters ${\ensuremath{\alpha}}_{i}$ are defined to express the interaction of a given atom in an alloy with the atoms of the ith shell of atoms surrounding it. From simple thermodynamic reasoning, involving a certain degree of approximation, equations relating the ${\ensuremath{\alpha}}_{i}$ with energy terms and the temperature are derived. Equations for the long-range order parameter, $S$, are obtained by considering the limiting case of $i$ very large. The values of the long- and short-range order parameters obtained by solving these equations are in good agreement with experimental values recently found by x-ray diffraction methods. The theory is extended to the calculation of configurational energy and specific heat, and to the determination of order parameters for alloys of arbitrary composition in such binary systems as that of the copper-gold alloys. In these cases qualitative agreement with experimental observations is obtained.
10
Order-Disorder Transformations in Alloys
Foster C. Nix, W. Shockley · Reviews of Modern Physics · 1938 · 393 citations
The propagation of order in co-operative phenomena
F. Zernike · Physica · 1940 · 325 citations
Order Theory, Emergent Phenomenon, Co-operative Phenomena +3